#include <stdio.h>

double series(unsigned int n)
{
    double term = 1.0, sum = 1.0;
    for(unsigned int k = 2; k <= n; ++k)
    {
        double a = k - 3. + (3.*k+1.)/(k*k+1.);
        sum += term *= a*a/k;
    }
    return sum;
}

int main()
{
    for(unsigned int n = 1; n <= 7; ++n)
        printf("%u: %.12lf\n",n,series(n));
}